Bonet, Javier ORCID: 0000-0002-0430-5181 , Gil, Antonio J. and Ortigosa, Rogelio (2016) On a tensor cross product based formulation of large strain solid mechanics. International Journal of Solids and Structures, 84. pp. 49-63. ISSN 0020-7683 (doi:https://doi.org/10.1016/j.ijsolstr.2015.12.030)

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Abstract

This paper describes in detail the formulation of large strain solid mechanics based on the tensor cross product, originally presented by R. de Boer, Vektor- und Tensorrechnung für Ingenieure, Springer-Verlag, 1982., page 76, and recently re-introduced by Bonet et al. in J. Bonet, A. J. Gil, R. Ortigosa, A computational framework for polyconvex large strain elasticity, Computer Methods in Applied Mechanics and Engineering 283 (2015) 1061 – 1094., and J. Bonet, A. J. Gil, C. H. Lee, M. Aguirre, R. Ortigosa, A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity, Computer Methods in Applied Mechanics and Engineering 283 (2015) 689 – 732. The paper shows how the tensor cross product facilitates the algebra associated with the area and volume maps between reference and final configurations. These maps, together with the fibre map, make up the fundamental kinematic variables in polyconvex elasticity. The algebra proposed leads to novel expressions for the tangent elastic operator which neatly separates material from geometrical dependencies. The paper derives new formulas for the spatial and material stress and their corresponding elasticity tensors. These are applied to the simple case of a Mooney-Rivlin material model. The extension to transversely isotropic material models is also considered.

Item Type:	Article
Additional Information:	© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords:	Large strain elasticity; Polyconvex elasticity; Complementary energy; Incompressible elasticity; Tensor cross product; Generalised Gibbs energy function
Subjects:	Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General)
Faculty / School / Research Centre / Research Group:	Vice-Chancellor's Group
Last Modified:	24 Apr 2018 14:31
URI:	http://gala.gre.ac.uk/id/eprint/14340

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